Geometry class used Geometer's Sketchpad as a discovery learning tool over the course of the year. During the third trimester, they tackled a mini-unit using Sketchpad that helped them discover relationships between the specials segments in the triangle. After discovering the relationships they then discovered the importance of the points of concurrency, especially with angle bisectors and perpendicular bisectors. Geometers Sketchpad is a wonderful tool.
Shared Lessons, Units, and Resources
Daily Lessons
Instructional Units
Other Related Resources
Algebra Technology Lessons
Geometry Unit Based Technology Activities (Main Unit)
The past year has been one of frustration and anxiety, not because of the use of the technology, but because I have now officially realized that meaningful discovery learning using technology in a math classroom is extremely expensive. I came into the E2T2 program with ideas abound about how to implement calculator based labs (CBL’s) along side of computer algebra systems (CAS), and computer geometry systems. These ideas, though, are tough to realize when each CBL system can be upwards of $100. Luckily GCMS has a CAS program on the Apple Computers and also Geometer’s sketchpad that allows for some discovery learning of some math concepts.
Previous to this program I had many activities developed that incorporated the above software, but I wanted to do and learn more. Through the classes and the research I was able to develop my skills with using wikis and blogs, and tried to brainstorm projects to incorporate in my math classroom. This is much easier said than done. The program introduced me to these things, and though I was unable to use these tools as a meaningful avenue for learning, I will strive to come up with new ideas to implement these activities into my classroom.
I was upset at my inability to come up with new ideas, because technology is a natural motivator and engager for students of all ages (including myself). I see this all the time when I use Grapher or SketchPad, but these were always isolated lessons. How can I capture this natural motivation and engage my 8th grade math students?
With this question in mind, I decided to make a mini unit on special segments within a triangle using Geometer’s SketchPad. I had already had a one-day lesson for this made, but I decided to revise it to be more in depth, and also add to it to include the points of concurrency and what their names are. The student’s, who had already shown a love for the program, loved that we could be in the lab for more than one day in a row. My direct teaching was minimal because they were so focused, and that allowed for awesome questioning opportunities.
Now I need to find some way to harness this into my pre-algebra classes using some Open Source software or some discounted hardware. These are the students that will benefit from it the most, but what activities can I do that will be meaningful, efficient, and affordable?
Literature Review
How does project-based learning connect to optimizing standard based learning within the math classroom? Sadly, even after reading through the book, Reinventing Project Based Learning: Your Field Guide to Real World Projects in the Digital Age by Suzie Boss and Jane Krauss, I do not know. The book offered very vague options and ideas in connecting technology to a specific math classroom instruction and objectives, and had little to no mention of how to utilize technology efficiently in an ever increasingly rigorous math classroom.
As I read through the book, I kept thinking “How can I use this specifically for my middle school math classroom?” I am well accustomed to using different pieces of hardware to help support a rigorous curriculum, but I am not well versed in implementing web-based software. My initial hope was to gain insight on how to increase my student’s performance using these tools. However, the book mainly focused on what these tools were, and not so much how to use them.
If there is a strength associated with this book it is the introduction of web based applications for a tech illiterate person. It introduces the use of wikis and blog to map out you or your students ideas. It introduces an option of screencasting to have students do tutorials, or give feedback on fellow students work. It also introduces the use of podcasts to openly share personal opinions of projects/events whenever the need arises. Still, the book did not offer specific ways to implement these strategies.
This book did not change any aspects of my philosophy on teaching. Prior to participating in E2T2 and reading this book, I had a very strong belief that technology is essential within a classroom in order to provide natural motivation and engagement to the students. I also believed that the proper and efficient use of technology will even allow a “difficult” learner to refocus attention on personal growth, and this was somewhat reinforced within the book. My philosophy on math not only includes the use of technology to build and reinforce concepts, but also technology to help practice basic skills that need to be mastered in order to discover the concepts. A program such as V-Math, or websites such as Mathiscool.com and Mathgames.com are great tools students can use to help build skills.
As mentioned previously, I really wanted to read about specific strategies for a math classroom. I truly felt the authors were purposely vague in order to market this book to more people. In doing so, though, they alienated all the persons, especially math folk, that want/need some ideas. Math classrooms are already having trouble engaging all students in meaningful lessons due to the pre-conceived notions that the students gain through communication with peers, parents, or media. What we/I want now is a specific way to use a wiki/ blog/ podcast/ screencast/etc for a specific objective. I realize some of the onus is on me to be creative, but without a model I have extreme difficulty coming up with fresh ideas.
Though I did not see many benefits to this book, I still see the importance of technology within a classroom. Hopefully, many more teachers, both incoming and tenured, will understand the strength of a well thought out technological lesson.
E2T2 Portfolio Page for Jeff Simon
Summary
Geometry class used Geometer's Sketchpad as a discovery learning tool over the course of the year. During the third trimester, they tackled a mini-unit using Sketchpad that helped them discover relationships between the specials segments in the triangle. After discovering the relationships they then discovered the importance of the points of concurrency, especially with angle bisectors and perpendicular bisectors. Geometers Sketchpad is a wonderful tool.Shared Lessons, Units, and Resources
technology based lessons taught over year)
Blog Entries
Simon Says...Student Work Samples
Summative Narrative
The past year has been one of frustration and anxiety, not because of the use of the technology, but because I have now officially realized that meaningful discovery learning using technology in a math classroom is extremely expensive. I came into the E2T2 program with ideas abound about how to implement calculator based labs (CBL’s) along side of computer algebra systems (CAS), and computer geometry systems. These ideas, though, are tough to realize when each CBL system can be upwards of $100. Luckily GCMS has a CAS program on the Apple Computers and also Geometer’s sketchpad that allows for some discovery learning of some math concepts.Previous to this program I had many activities developed that incorporated the above software, but I wanted to do and learn more. Through the classes and the research I was able to develop my skills with using wikis and blogs, and tried to brainstorm projects to incorporate in my math classroom. This is much easier said than done. The program introduced me to these things, and though I was unable to use these tools as a meaningful avenue for learning, I will strive to come up with new ideas to implement these activities into my classroom.
I was upset at my inability to come up with new ideas, because technology is a natural motivator and engager for students of all ages (including myself). I see this all the time when I use Grapher or SketchPad, but these were always isolated lessons. How can I capture this natural motivation and engage my 8th grade math students?
With this question in mind, I decided to make a mini unit on special segments within a triangle using Geometer’s SketchPad. I had already had a one-day lesson for this made, but I decided to revise it to be more in depth, and also add to it to include the points of concurrency and what their names are. The student’s, who had already shown a love for the program, loved that we could be in the lab for more than one day in a row. My direct teaching was minimal because they were so focused, and that allowed for awesome questioning opportunities.
Now I need to find some way to harness this into my pre-algebra classes using some Open Source software or some discounted hardware. These are the students that will benefit from it the most, but what activities can I do that will be meaningful, efficient, and affordable?
Literature Review
How does project-based learning connect to optimizing standard based learning within the math classroom? Sadly, even after reading through the book, Reinventing Project Based Learning: Your Field Guide to Real World Projects in the Digital Age by Suzie Boss and Jane Krauss, I do not know. The book offered very vague options and ideas in connecting technology to a specific math classroom instruction and objectives, and had little to no mention of how to utilize technology efficiently in an ever increasingly rigorous math classroom.As I read through the book, I kept thinking “How can I use this specifically for my middle school math classroom?” I am well accustomed to using different pieces of hardware to help support a rigorous curriculum, but I am not well versed in implementing web-based software. My initial hope was to gain insight on how to increase my student’s performance using these tools. However, the book mainly focused on what these tools were, and not so much how to use them.
If there is a strength associated with this book it is the introduction of web based applications for a tech illiterate person. It introduces the use of wikis and blog to map out you or your students ideas. It introduces an option of screencasting to have students do tutorials, or give feedback on fellow students work. It also introduces the use of podcasts to openly share personal opinions of projects/events whenever the need arises. Still, the book did not offer specific ways to implement these strategies.
This book did not change any aspects of my philosophy on teaching. Prior to participating in E2T2 and reading this book, I had a very strong belief that technology is essential within a classroom in order to provide natural motivation and engagement to the students. I also believed that the proper and efficient use of technology will even allow a “difficult” learner to refocus attention on personal growth, and this was somewhat reinforced within the book. My philosophy on math not only includes the use of technology to build and reinforce concepts, but also technology to help practice basic skills that need to be mastered in order to discover the concepts. A program such as V-Math, or websites such as Mathiscool.com and Mathgames.com are great tools students can use to help build skills.
As mentioned previously, I really wanted to read about specific strategies for a math classroom. I truly felt the authors were purposely vague in order to market this book to more people. In doing so, though, they alienated all the persons, especially math folk, that want/need some ideas. Math classrooms are already having trouble engaging all students in meaningful lessons due to the pre-conceived notions that the students gain through communication with peers, parents, or media. What we/I want now is a specific way to use a wiki/ blog/ podcast/ screencast/etc for a specific objective. I realize some of the onus is on me to be creative, but without a model I have extreme difficulty coming up with fresh ideas.
Though I did not see many benefits to this book, I still see the importance of technology within a classroom. Hopefully, many more teachers, both incoming and tenured, will understand the strength of a well thought out technological lesson.